Dear all, am trying to solve a solid mechanics problem but I observe that the problem setup does not possess displacement boundary condition i.e. there is no point in/on the problem domain where displacement (u) equal zero.
Please share your thoughts on this. Thanks
Dear Ademiloye,
if you don't apply any Dirichlet type BC to your problem, the matrix generally becomes singular and is not invertible.
In terms of solid mechanics we understand that as the exclusion of rigid body movements (proper statical support). As Christoph said, the value at the BC does not have to be zero, but must have prescribed values at some points.
If you really need to solve the problem without any Dirichlet BC, you'll have to formulate in terms of dynamics. That gives you the difficulty of proper time integration and possibly problems with conservation of energy.
hope that brings you a bit further
Thanks @Saeed
My non-linear equation is a generic equation in which I used the deformation gradient tensor and PK stress tensor to formulate the Strain energy density function. This was then written in weak form and subsequently linearized to give an incremental matrix equation of the form (KU = F_external - F_internal).
I understand that the essential boundary conditions are usually imposed in many solid mechanics problems when using FEM or Meshfree methods but in my case I observed that this condition is not applicable since there is no point in/on the problem domain where displacement (u) equal zero.
I have also search literature to see if anyone solve any similar problem in the past but I couldn't find any hence I decided to ask erudite scholars on RG.
Thanks once again.
@Christoph, thank you for your answer but have you seen any problem like this in literature, if yes, please refer me. Thanks
Dear Ademiloye,
if you don't apply any Dirichlet type BC to your problem, the matrix generally becomes singular and is not invertible.
In terms of solid mechanics we understand that as the exclusion of rigid body movements (proper statical support). As Christoph said, the value at the BC does not have to be zero, but must have prescribed values at some points.
If you really need to solve the problem without any Dirichlet BC, you'll have to formulate in terms of dynamics. That gives you the difficulty of proper time integration and possibly problems with conservation of energy.
hope that brings you a bit further
Since the finite element method uses the displacement method , at least an node must be bonded otherwise the model walks to the infinity.
Regards
Dear Mr. Adeliloye,
Is the problem you are considering already in equilibrium (although without any presribed displacement/ support)? If yes, in the finite element analysis you can impose minimum displacement boundary conditions (for example a hinge and a roller in the problem is 2D), merely to prevent the rigid body displacements. The results will be completely equivalent to the results of the original problem.
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